Allardyce’s contract runs out at the end of the season but as of yet he has still not been offered a new deal.
The meeting will be with West Ham co-chairmen David Sullivan and David Gold, along with vice-chairwoman Karren Brady.
West Ham are 11th in the Premier League and have won just three of their Premier League games this year.
In March this year,??Brady warned the manager that his team were ???underachieving???, but Allardyce said she was wrong and??was quick to defend his players.
Allardyce said earlier this week: “I’ve never heard them say I’m not doing a good job. I’ll find out next week and then I can ask them why – see if they give me an honest answer.
“We’re 11th with 47 points so we’ve got to try and get that 50-point mark and hope it gets us to 10th.
“Even if it doesn’t it’s still been an outstanding season and for me an outstanding three years back in the Premier League. I’ve only had to worry about relegation for about six weeks in three seasons.”
The crucial meeting will take place the day after West Ham???s last game of the season, away at Newcastle United.
Victory could see Allardyce consign his former club to relegation and perhaps secure his future at Upton Park.
Napoli manager Rafa Bentiez is currenly odds-on favourite to replace Allardyce.